Characterization of Stress-Diffusion Coupling in Lithiated Germanium by Nanoindentation

Abstract

There is currently a growing demand for low-cost, high-performance electrochemical energy storage solutions to consumer electronics, vehicle electrification and stationary power management. The successful development and deployment of such solutions necessitate a fundamental understanding of the mechanical properties of electrochemical materials, as well as the intricate coupling between the electro-chemo-mechanical processes in these materials. In this work, we performed a combined experimental and modelling investigation of the stress-diffusion coupling behavior of lithiated germanium (Ge) for its use in high-performance lithium-ion batteries. Thin films of Ge were fabricated using sputtering deposition and then electrochemically lithiated, after which they were subjected to nanoindentation at varying load levels to study indentation-induced creep deformation. Concurrently, a continuum chemo-mechanical model of the nanoindentation test was developed and used to investigate the fundamental mechanisms underlying the stress-gradient-driven creep deformation. The stress-diffusion coupling coefficient and diffusivity of lithium in Ge were obtained by quantitatively comparing the simulated nanoindentation response with the experimental measurements. This integrative experimental and computation work provides important insights into the chemo-mechanical coupling process in high-performance rechargeable battery electrodes.

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References

  1. 1.

    Dunn B, Kamath H, Tarascon J-M (2011) Electrical energy storage for the grid: a battery of choices. Science 334:928–935

    Article  Google Scholar 

  2. 2.

    Liu XH, Huang S, Picraux ST, Li J, Zhu T, Huang JY (2011) Reversible nanopore formation in Ge nanowires during lithiation–delithiation cycling: an in situ transmission electron microscopy study. Nano Lett 11:3991–3997

    Article  Google Scholar 

  3. 3.

    Liu XH, Liu Y, Kushima A, Zhang S, Zhu T, Li J, Huang JY (2012) In situ TEM experiments of electrochemical lithiation and delithiation of individual nanostructures. Adv Energy Mater 2:722–741

    Article  Google Scholar 

  4. 4.

    Liu XH, Wang JW, Huang S, Fan F, Huang X, Liu Y, Krylyuk S, Yoo J, Dayeh SA, Davydov AV (2012) In situ atomic-scale imaging of electrochemical lithiation in silicon. Nat Nanotechnol 7:749–756

    Article  Google Scholar 

  5. 5.

    McDowell MT, Lee SW, Harris JT, Korgel BA, Wang C, Nix WD, Cui Y (2013) In situ TEM of two-phase Lithiation of amorphous silicon Nanospheres. Nano Lett 13:758–764

    Article  Google Scholar 

  6. 6.

    Wang JW, He Y, Fan F, Liu XH, Xia S, Liu Y, Harris CT, Li H, Huang JY, Mao SX (2013) Two-phase electrochemical lithiation in amorphous silicon. Nano Lett 13:709–715

    Article  Google Scholar 

  7. 7.

    Wang J, Fan F, Liu Y, Jungjohann KL, Lee SW, Mao SX, Liu X, Zhu T (2014) Structural evolution and pulverization of tin nanoparticles during lithiation-delithiation cycling. J Electrochem Soc 161:F3019–F3024

    Article  Google Scholar 

  8. 8.

    Nadimpalli SP, Sethuraman VA, Bucci G, Srinivasan V, Bower AF, Guduru PR (2013) On plastic deformation and fracture in Si films during electrochemical lithiation/delithiation cycling. J Electrochem Soc 160:A1885–A1893

    Article  Google Scholar 

  9. 9.

    Gonzalez J, Sun K, Huang M, Lambros J, Dillon S, Chasiotis I (2014) Three dimensional studies of particle failure in silicon based composite electrodes for lithium ion batteries. J Power Sources 269:334–343

    Article  Google Scholar 

  10. 10.

    Gonzalez J, Sun K, Huang M, Dillon S, Chasiotis I, Lambros J (2015) X-ray microtomography characterization of Sn particle evolution during lithiation/delithiation in lithium ion batteries. J Power Sources 285:205–209

    Article  Google Scholar 

  11. 11.

    Sethuraman VA, Srinivasan V, Bower AF, Guduru PR (2010) In situ measurements of stress-potential coupling in lithiated silicon. J Electrochem Soc 157:A1253–A1261

    Article  Google Scholar 

  12. 12.

    Sethuraman VA, Chon MJ, Shimshak M, Srinivasan V, Guduru PR (2010) In situ measurements of stress evolution in silicon thin films during electrochemical lithiation and delithiation. J Power Sources 195:5062–5066

    Article  Google Scholar 

  13. 13.

    Chon MJ, Sethuraman VA, McCormick A, Srinivasan V, Guduru PR (2011) Real-time measurement of stress and damage evolution during initial lithiation of crystalline silicon. Phys Rev Lett 107:045503

    Article  Google Scholar 

  14. 14.

    Sethuraman VA, Nguyen A, Chon MJ, Nadimpalli SP, Wang H, Abraham DP, Bower AF, Shenoy VB, Guduru PR (2013) Stress evolution in composite silicon electrodes during lithiation/delithiation. J Electrochem Soc 160:A739–A746

    Article  Google Scholar 

  15. 15.

    Bucci G, Nadimpalli SP, Sethuraman VA, Bower AF, Guduru PR (2014) Measurement and modeling of the mechanical and electrochemical response of amorphous Si thin film electrodes during cyclic lithiation. J Mech Phys Solids 62:276–294

    Article  Google Scholar 

  16. 16.

    Nadimpalli SP, Tripuraneni R, Sethuraman VA (2015) Real-time stress measurements in germanium thin film electrodes during electrochemical lithiation/delithiation cycling. J Electrochem Soc 162:A2840–A2846

    Article  Google Scholar 

  17. 17.

    Pharr M, Choi YS, Lee D, Oh KH, Vlassak JJ (2016) Measurements of stress and fracture in germanium electrodes of lithium-ion batteries during electrochemical lithiation and delithiation. J Power Sources 304:164–169

    Article  Google Scholar 

  18. 18.

    Chen C-H, Chason E, Guduru PR (2017) Measurements of the phase and stress evolution during initial Lithiation of Sn electrodes. J Electrochem Soc 164:A574–A579

    Article  Google Scholar 

  19. 19.

    Sethuraman VA, Chon MJ, Shimshak M, Van Winkle N, Guduru PR (2010) In situ measurement of biaxial modulus of Si anode for li-ion batteries. Electrochem Commun 12:1614–1617

    Article  Google Scholar 

  20. 20.

    Wang X, Fan F, Wang J, Wang H, Tao S, Yang A, Liu Y, Beng Chew H, Mao SX, Zhu T, Xia S (2015) High damage tolerance of electrochemically lithiated silicon. Nat Commun 6:8417

    Article  Google Scholar 

  21. 21.

    Wang X, Yang A, Xia S (2016) Fracture toughness characterization of Lithiated germanium as an anode material for lithium-ion batteries. J Electrochem Soc 163:A90–A95

    Article  Google Scholar 

  22. 22.

    Pharr M, Suo Z, Vlassak JJ (2013) Measurements of the fracture energy of lithiated silicon electrodes of li-ion batteries. Nano Lett 13:5570–5577

    Article  Google Scholar 

  23. 23.

    Liu XH, Fan F, Yang H, Zhang S, Huang JY, Zhu T (2013) Self-limiting lithiation in silicon nanowires. ACS Nano 7:1495–1503

    Article  Google Scholar 

  24. 24.

    Haftbaradaran H, Gao H, Curtin W (2010) A surface locking instability for atomic intercalation into a solid electrode. Appl Phys Lett 96:091909

    Article  Google Scholar 

  25. 25.

    Gu M, Yang H, Perea DE, Zhang J-G, Zhang S, Wang C-M (2014) Bending-induced symmetry breaking of Lithiation in germanium nanowires. Nano Lett 14:4622–4627

    Article  Google Scholar 

  26. 26.

    Bhandakkar TK, Johnson HT (2012) Diffusion induced stresses in buckling battery electrodes. J Mech Phys Solids 60:1103–1121

    MathSciNet  Article  Google Scholar 

  27. 27.

    Zhang J, Lu B, Song Y, Ji X (2012) Diffusion induced stress in layered li-ion battery electrode plates. J Power Sources 209:220–227

    Article  Google Scholar 

  28. 28.

    Cannarella J, Leng CZ, Arnold CB (2014) On the coupling between stress and voltage in lithium-ion pouch cells. In: Proc. of SPIE, pp 91150K

  29. 29.

    Jacques E, Lindbergh GR, Zenkert D, Leijonmarck S, Kjell MH (2015) Piezo-electrochemical energy harvesting with lithium-intercalating carbon fibers. ACS Appl Mater Interfaces 7:13898–13904

    Article  Google Scholar 

  30. 30.

    Cannarella J, Arnold CB (2015) Toward low-frequency mechanical energy harvesting using energy-dense Piezoelectrochemical materials. Adv Mater 27:7440–7444

    Article  Google Scholar 

  31. 31.

    Kim S, Choi SJ, Zhao K, Yang H, Gobbi G, Zhang S, Li J (2016) Electrochemically driven mechanical energy harvesting. Nat Commun 7:10146

    Article  Google Scholar 

  32. 32.

    Schiffer Z, Arnold C (2017) Characterization and model of Piezoelectrochemical energy harvesting using Lithium ion batteries. Exp Mech. https://doi.org/10.1007/s11340-017-0291-1

  33. 33.

    Gueshi T, Tokuda K, Matsuda H (1978) Voltammetry at partially covered electrodes: part I. Chronopotentiometry and chronoamperometry at model electrodes. J Electroanal Chem Interfacial Electrochem 89:247–260

    Article  Google Scholar 

  34. 34.

    Fung Y, Chad S (1993) Investigation of the 1-methyl-3-ethylimidazolium chloride-AlCl3/LiAlCl4 system for lithium battery application part I: physical properties and preliminary chronopotentiometric study. J Appl Electrochem 23:346–351

    Article  Google Scholar 

  35. 35.

    Gueshi T, Tokuda K, Matsuda H (1979) Voltammetry at partially covered electrodes: part II. Linear potential sweep and cyclic voltammetry. J Electroanal Chem Interfacial Electrochem 101:29–38

    Article  Google Scholar 

  36. 36.

    Itagaki M, Kobari N, Yotsuda S, Watanabe K, Kinoshita S, Ue M (2004) In situ electrochemical impedance spectroscopy to investigate negative electrode of lithium-ion rechargeable batteries. J Power Sources 135:255–261

    Article  Google Scholar 

  37. 37.

    Kuriyama N, Sakai T, Miyamura H, Uehara I, Ishikawa H, Iwasaki T (1992) Electrochemical impedance spectra and deterioration mechanism of metal hydride electrodes. J Electrochem Soc 139:L72–L73

    Article  Google Scholar 

  38. 38.

    Hertzberg B, Benson J, Yushin G (2011) Ex-situ depth-sensing indentation measurements of electrochemically produced Si–li alloy films. Electrochem Commun 13:818–821

    Article  Google Scholar 

  39. 39.

    Ratchford JB, Crawford BA, Wolfenstine J, Allen JL, Lundgren CA (2012) Young's modulus of polycrystalline Li12Si7 using nanoindentation testing. J Power Sources 211:1–3

    Article  Google Scholar 

  40. 40.

    Ratchford JB, Schuster BE, Crawford BA, Lundgren CA, Allen JL, Wolfenstine J (2011) Young's modulus of polycrystalline Li22Si5. J Power Sources 196:7747–7749

    Article  Google Scholar 

  41. 41.

    Zinn A-H, Borhani-Haghighi S, Ventosa E, Pfetzing-Micklich J, Wieczorek N, Schuhmann W, Ludwig A (2014) Mechanical properties of SiLix thin films at different stages of electrochemical li insertion. Phys Status Solidi A 211:2650–2656

    Article  Google Scholar 

  42. 42.

    Berla LA, Lee SW, Cui Y, Nix WD (2015) Mechanical behavior of electrochemically lithiated silicon. J Power Sources 273:41–51

    Article  Google Scholar 

  43. 43.

    Fuller C, Severiens J (1954) Mobility of impurity ions in germanium and silicon. Phys Rev 96:21

    Article  Google Scholar 

  44. 44.

    Jung SC, Choi JW, Han Y-K (2012) Anisotropic volume expansion of crystalline silicon during electrochemical lithium insertion: an atomic level rationale. Nano Lett 12:5342–5347

    Article  Google Scholar 

  45. 45.

    Lee SW, McDowell MT, Berla LA, Nix WD, Cui Y (2012) Fracture of crystalline silicon nanopillars during electrochemical lithium insertion. Proc Natl Acad Sci 109:4080–4085

    Article  Google Scholar 

  46. 46.

    Lee SW, Ryu I, Nix WD, Cui Y (2015) Fracture of crystalline germanium during electrochemical lithium insertion. Extreme Mechanics Letters 2:15–19

    Article  Google Scholar 

  47. 47.

    Liang W, Yang H, Fan F, Liu Y, Liu XH, Huang JY, Zhu T, Zhang S (2013) Tough germanium nanoparticles under electrochemical cycling. ACS Nano 7:3427–3433

    Article  Google Scholar 

  48. 48.

    Graetz J, Ahn CC, Yazami R, Fultz B (2004) Nanocrystalline and thin film germanium electrodes with high lithium capacity and high rate capabilities. J Electrochem Soc 151:A698–A702

    Article  Google Scholar 

  49. 49.

    Pinson MB, Bazant MZ (2013) Theory of SEI formation in rechargeable batteries: capacity fade, accelerated aging and lifetime prediction. J Electrochem Soc 160:A243–A250

    Article  Google Scholar 

  50. 50.

    Fischer-Cripps AC (2004) Nanoindentation, 2nd edn. Springer-Verlag, New York City

  51. 51.

    Neale MJ (1995) The tribology handbook. Butterworth-Heinemann, Oxford

    Google Scholar 

  52. 52.

    Larcht'e F, Cahn J (1982) The effect of self-stress on diffusion in solids. Acta Metall 30:1835–1845

    Article  Google Scholar 

  53. 53.

    Bower AF, Guduru PR, Sethuraman VA (2011) A finite strain model of stress, diffusion, plastic flow, and electrochemical reactions in a lithium-ion half-cell. J Mech Phys Solids 59:804–828

    MathSciNet  Article  MATH  Google Scholar 

  54. 54.

    Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583

    Article  Google Scholar 

  55. 55.

    Shenoy VB, Johari P, Qi Y (2010) Elastic softening of amorphous and crystalline li–Si phases with increasing li concentration: a first-principles study. J Power Sources 195:6825–6830

    Article  Google Scholar 

  56. 56.

    Qi Y, Hector LG, James C, Kim KJ (2014) Lithium concentration dependent elastic properties of battery electrode materials from first principles calculations. J Electrochem Soc 161:F3010–F3018

    Article  Google Scholar 

  57. 57.

    Zeng Z, Liu N, Zeng Q, Ding Y, Qu S, Cui Y, Mao WL (2013) Elastic moduli of polycrystalline Li15Si4 produced in lithium ion batteries. J Power Sources 242:732–735

    Article  Google Scholar 

  58. 58.

    Schuh CA, Hufnagel TC, Ramamurty U (2007) Mechanical behavior of amorphous alloys. Acta Mater 55:4067–4109

    Article  Google Scholar 

  59. 59.

    Ding N, Xu J, Yao Y, Wegner G, Fang X, Chen C, Lieberwirth I (2009) Determination of the diffusion coefficient of lithium ions in nano-Si. Solid State Ionics 180:222–225

    Article  Google Scholar 

  60. 60.

    Tritsaris GA, Zhao K, Okeke OU, Kaxiras E (2012) Diffusion of lithium in bulk amorphous silicon: a theoretical study. J Phys Chem C 116:22212–22216

    Article  Google Scholar 

  61. 61.

    Gao Y, Zhou M (2011) Strong stress-enhanced diffusion in amorphous lithium alloy nanowire electrodes. J Appl Phys 109:014310

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge the supports of the National Science Foundation (Grants CMMI-1300458 and CMMI-1554393). This work was performed in part at the Georgia Tech Institute for Electronics and Nanotechnology, a member of the National Nanotechnology Coordinated Infrastructure, which is supported by the National Science Foundation (Grant ECCS-1542174).

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Correspondence to S. Xia.

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Papakyriakou, M., Wang, X. & Xia, S. Characterization of Stress-Diffusion Coupling in Lithiated Germanium by Nanoindentation. Exp Mech 58, 613–625 (2018). https://doi.org/10.1007/s11340-018-0382-7

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Keywords

  • Rechargeable batteries
  • Electrode materials
  • Stress-diffusion coupling
  • Nanoindentation
  • Chemo-mechanical modelling